ABSTRACT. We introduce a novel probabilistic algorithm (CPRM) for real-time motion planning in the configuration space C. Our algorithm differs from a Probabilistic Road Map algorithm (PRM) in the motion between a pair of anchoring points (local planner) which takes place on the boundary of the obstacle subspace O. We define a varying potential field f on ∂O as a Morse function and follow ∇f . We then exemplify our algorithm on a redundant worm climbing robot with n degrees of freedom and compare our algorithm running results with those of PRM.

Certain species of ants can carry out tasks in dense work spaces while maintaining their ability to accurately manipulate heavy loads, and these advantages are of interest to the robotics community. We consider a robotic swarm of N ≥ 6 agents that assumes the task of moving a load through a cluttered space. This forces the swarm to carefully manipulate the orientation of the load, while transporting it to its destination point. We model this scenario as a 6-PPSS (Prismatic-Prismatic-Spherical-Spherical) redundant mobile platform, having six degrees of freedom. As with insects, the multitude of agents enables sharing the burden of the load in the case that one or more agents are blocked by an obstacle. We model this by a semi-algebraic set of constraints on the distances between the agents and the load. We apply an Extended Kalman Filter routine, in order to estimate their relative locations. We show how the estimation-error is reduced when position-information is shared among the agents. These estimations are then used to calculate the full configuration and investigate the effect of position estimation error on the platform heading error. We show how motion planning can then be calculated in the model's full configuration space and demonstrate this with a distributed control scheme. To reduce the search time, we introduce a variant of the crawling probabilistic road map motion planning algorithm under a set of kinematic constraints and work-space obstacles. Finally, we exemplify our algorithms on several simulated scenarios. INDEX TERMS Swarm, load, extended Kalman filter, parallel platform, crawling probabilistic road map.

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Recent years show an increasing interest in flexible robots due to their adaptability merits. This paper introduces a novel set of hyper-redundant flexible robots which we call actuated flexible manifold (AFM). The AFM is a two-dimensional hyper-redundant grid surface embedded in ℝ2 or ℝ3. Theoretically, such a mechanism can be manipulated into any continuous smooth function. We introduce the mathematical framework for the kinematics of an AFM. We prove that for a nonsingular configuration, the number of degrees of freedom (DOF) of an AFM is simply the number of its grid segments. We also show that for a planar rectangular grid, every nonsingular configuration that is also energetically stable is isolated. We show how to calculate the forward and inverse kinematics for such a mechanism. Our analysis is also applicable for three-dimensional hyper-redundant structures as well. Finally, we demonstrate our solution on some actuated flexible grid-shaped surfaces.

Exact motion planning for hyper-redundant robots under complex constraints is computationally intractable. This paper does not deal with the optimization of motion planning algorithms, but rather with the simplification of the configuration space presented to the algorithms. We aim to reduce the configuration space so that the robot's embedded motion planning system will be able to store and access an otherwise immense data file. We use a n-DCT compression algorithm together with a Genetic based compression algorithm, in order to reduce the complexity of motion planning computations and reduce the need for memory. We exemplify our algorithm on a hyperredundant worm-like climbing robot with six degrees of freedom (DOF).